{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Locally weighted linear regression\n",
    "\n",
    "## (a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### i."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $W:= \\operatorname{diag}\\left(w^{(1)}, \\ldots, w^{(m)}\\right)$ and $z:= X\\theta-y$, where $X:= (x^{(1)}, \\ldots, x^{(m)})^T$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then \n",
    "$$\\begin{align*}\n",
    "2J(\\theta) &= \\sum_{i=1}^m w^{(i)} \\left(\\theta^Tx^{(i)} - y^{(i)}\\right)^2\\\\\n",
    "&= \\sum_{i=1}^m w^{(i)} \\left(z^{(i)} \\right)^2\\\\\n",
    "&= z^TWz\\\\\n",
    "&= (X\\theta-y)^TW(X\\theta-y).\n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Remark**: The way problem i is phrased, we actually should use $\\frac {1}{2} W$ instead of $W$. But it is more convenient to work with the formula $J(\\theta) = \\frac {1}{2} (X\\theta-y)^TW(X\\theta-y)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ii."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The differential is \n",
    "$$ \\mathrm d_\\theta J(\\theta) = (X\\theta-y)^TWX$$\n",
    "and hence the gradient is given by (because $W $ is a diagonal matrix we have $W^T=W$)\n",
    "$$\\nabla_\\theta J(\\theta) = X^TW(X\\theta-y)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Setting the gradient to $0$ gives \n",
    "$$ \\begin{align*}\n",
    "&& 0 &= (X^TWX)\\theta - X^TWy\\\\\n",
    "&\\Leftrightarrow & \\theta &= (X^TWX)^{-1}X^TWy. \n",
    "\\end{align*}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### iii.\n",
    "\n",
    "The likelihood of $\\theta$ is given by \n",
    "$$ \\prod_{i=1}^m p(y^{(i)}\\mid x^{(i)};\\theta) = \\frac 1{\\left(\\sqrt{2\\pi}\\right)^m\\sigma^{(1)}\\cdots \\sigma^{(m)}} \\exp\\left( \n",
    "-\\frac {1}{2}\\sum_{i=1}^m \\frac 1{(\\sigma^{(i)})^2} \\left(y^{(i)}-\\theta^Tx^{(i)}\\right)^2 \n",
    "\\right).$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore maximizing the likelihood of $\\theta$ is equivalent to minimizing \n",
    "$$ \\frac {1}{2}\\sum_{i=1}^m w^{(i)} \\left(\\theta^Tx^{(i)} - y^{(i)}\\right)^2,$$\n",
    "where \n",
    "$$w^{(i)}:= \\frac 1{(\\sigma^{(i)})^2}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import src.util as util\n",
    "\n",
    "from src.linear_model import LinearModel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau=5e-1\n",
    "train_path='data/ds5_train.csv'\n",
    "eval_path='data/ds5_valid.csv'\n",
    "test_path='data/ds5_test.csv'\n",
    "x_train, y_train = util.load_dataset(train_path, add_intercept=True)\n",
    "x_val, y_val = util.load_dataset(eval_path, add_intercept=True)\n",
    "x_test, y_test = util.load_dataset(train_path, add_intercept=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take a look at the trainingset:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((300, 2), (300,))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, y_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x264b2a396a0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x_train[:,1], y_train, 'bx')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "class LocallyWeightedLinearRegression(LinearModel):\n",
    "    \"\"\"Locally Weighted Regression (LWR).\n",
    "\n",
    "    Example usage:\n",
    "        > clf = LocallyWeightedLinearRegression(tau)\n",
    "        > clf.fit(x_train, y_train)\n",
    "        > clf.predict(x_eval)\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, tau):\n",
    "        super(LocallyWeightedLinearRegression, self).__init__()\n",
    "        self.tau = tau\n",
    "        self.x = None\n",
    "        self.y = None\n",
    "\n",
    "    def fit(self, x, y):\n",
    "        \"\"\"Fit LWR by saving the training set.\n",
    "\n",
    "        \"\"\"\n",
    "        # *** START CODE HERE ***\n",
    "        self.x = x\n",
    "        self.y = y\n",
    "        # *** END CODE HERE ***\n",
    "\n",
    "    def predict(self, x):\n",
    "        \"\"\"Make predictions given inputs x.\n",
    "\n",
    "        Args:\n",
    "            x: Inputs of shape (m, n).\n",
    "\n",
    "        Returns:\n",
    "            Outputs of shape (m,).\n",
    "        \"\"\"\n",
    "        # *** START CODE HERE ***\n",
    "        m,n = x.shape\n",
    "        m_train, = self.y.shape\n",
    "\n",
    "        # make a (m,m_train,n) array d \n",
    "        # so that d[i] is an array of shape (m_train,n) that \n",
    "        # contains the differences between \n",
    "        # x[i] and the training examples\n",
    "        d = x.reshape((m,1,n)) - self.x\n",
    "        \n",
    "        # shape (m, m_train) array \n",
    "        # with the norms of these differences\n",
    "        d_normed = np.linalg.norm(d, ord=2, axis=2) \n",
    "        \n",
    "        # shape (m, m_train) tensor \n",
    "        # such that w[i] is a an (m_train,) array\n",
    "        # that contains the local weights of x[i]\n",
    "        w = np.exp(-1/(2*self.tau**2)* d_normed)\n",
    "        \n",
    "        #turn w into diagonal matrices\n",
    "        # W has shape (m,m_train, m_train)\n",
    "        W = np.apply_along_axis(np.diag, axis=1, arr=w)     \n",
    "        \n",
    "        # compute theta with the formula from (a)ii.\n",
    "        # theta has shape (m,n,1)\n",
    "        theta = np.linalg.inv(self.x.T @ W @ self.x) @ self.x.T @ W @ self.y.reshape((-1,1))\n",
    "        \n",
    "        # return an array of shape (m,)\n",
    "        return np.ravel(x.reshape((m,1,n)) @ theta )\n",
    "        # *** END CODE HERE ***\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit a model to the training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "clf = LocallyWeightedLinearRegression(tau)\n",
    "clf.fit(x_train,y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute predictions on the validation set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_pred = clf.predict(x_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compute the mean squared error:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2929604606620909"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def mse(y_p,y):\n",
    "    return np.mean((y_p -y)**2)\n",
    "\n",
    "mse(y_pred,y_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the predictions on the validation set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_predictions(x, y_p, y):\n",
    "    plt.figure()\n",
    "    plt.plot(x[:,1], y, 'bx')\n",
    "    plt.plot(x[:,1], y_p, 'ro')\n",
    "\n",
    "plot_predictions(x_val, y_pred, y_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model seems to be underfitting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## (c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "tau_values=[3e-2, 5e-2, 1e-1, 5e-1, 1e0, 1e1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Train  multiple models and plot their predictions on the validation set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "models = []\n",
    "mse_values = []\n",
    "\n",
    "for tau in tau_values:\n",
    "    model = LocallyWeightedLinearRegression(tau)\n",
    "    models.append(model)\n",
    "    model.fit(x_train, y_train)\n",
    "    y_p = model.predict(x_val)\n",
    "    mse_values.append(mse(y_p, y_val))\n",
    "    plot_predictions(x_val, y_p, y_val)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Find the best value for $\\tau$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "best tau: 0.1\n"
     ]
    }
   ],
   "source": [
    "best_i = np.argmin(mse_values)\n",
    "best_tau = tau_values[best_i]\n",
    "best_model = models[best_i]\n",
    "\n",
    "print(\"best tau:\", best_tau)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mean square error for $\\tau = 0.1$ on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.003187171325722038"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_pred = best_model.predict(x_test)\n",
    "mse(y_pred, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's also plot the predictions on the test set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HH8IiF+pGi4G1EbbfKMfQExiXTkB4F9vO4KIfu1tIQNZqHNRqRPcVLLow0NmohdFjueCRJ862tm71L1blBIP08dNpw9ny9d2unUKh799U6ER5jPCavTSY2hpAScEIflAEWBZx+9R1qdDXi+lpvqUZJsbamYxcLXTfQJyaRQ2AFlk5UREXznE1BtqziBsDEZrxEOmVgNWDpV3ePvylXcaHHwQj+AERFdvdWSBKpuDwGp10NinXYkJacLbxzp1E74W1NinJ+y6SlCo/Pe2TIKTJJGscLO1aj9K5hLwR+z4wgh8QIYLvU79EiugGzODVIpqnxGm7GELInIzUoSH7sVcWpaqmH6HQpJGGanSsA5UEjOAHRYAP30+ApYhuH00c4hx5dGFZth+60y8bwlXh/t5qNbsMATfcM4liqVmVSxXoWgcqCRjB74dO0e9z1o9XJM1pNi1cdIOKg+rKiZz9PI1S3xdz50hpaor4TduTJpaW5T0S0qRbWRw4Yr/WkJ0pMFASjBH8GPHtIypDdIMO/1VbjT43wigurbXJW7bB+/iSJJa8LmylUjL2XxBrYbcd34Womjppxwh+nPiJugTRDdqoutfIQzoSjr1XeOba9pMiEqpvyjphvovQ+Am+ybQVzdiYnRFYLgOM2Y+zs8DYGIiT2chbH4STew9gBe1Zpyso4uTeA23reBmu3MxX0XhlxxaL9vqQOBmaQ6c43x9jwIkT9m+SBHjngSYZsXFCi5xrhbPeEBDenUD1klgL34eg1ni/BJoXUO3Dd/ZBRix4SqxBv/MjSfWARJCU/BIdgXHpBEdq9TyJohsohC1ByTd90Uekks7wSnYf3WNlL1IlIRnkOmIEvw+k18mXILr9hLBpkYAlmpRY+ETto7XnUaZDt6ZM7Ps5/xNSI0o3pAs+gHcC+A6A7wH4hMfr9wE4BeBbreXXem1TmUsnYeLRb2y/qgQsqTeaAJFKSbqpOaO1224LMGpLEn2OcE0sfjikCj6APIDvA3gzgA0Avg3g+o733AfgkX62q6oevopm41EII6QqLiQnfHJlW5mIMVrZJrDrUo92lTr3COjE2dfxcfuUGx9Pzr73pA9jSovMcEHEPaqWLfi3APia6/kDAB7oeE8iBL9WI1rKlRNl4Ycl9rR1y6JGvj3TtpHvvwIkb9udluPlwSJNbLa0tQ69RGBmxj6MmZn11oTuR92OoW/6MKbS5HqM++YlW/B/BcAXXM/HO8W9Jfj/CODvAPwpgGs525oAsABgYfv27XK+jR4c3WPRazH2ulWBkqEyr45OqSRm+52+4Wp1zf/b2RdVpXA4Qua+6CcmiD79VosWme27P3NlmY7uWa+9pKzpuGgS5i4VSZzXnGzBf4+H4H+24z0lAIOtvz8EoNZruyqjdA7datHzsC++NPS4dDMxYRcbc1sbIyP2eql4XejOIhqru7zwpfyGtebmKq1l9+cf22+LfAPoqgWUNiODiPQIDfZB1qjC2a57VJ1ql07H+/MAlnttV5XgR74Tax76ODFhFxtzC/7wsHzBF1V6Ogirw96jiSagRU0WXi3/2CxfReeo7g3DZc0z1WpEH9i4PoJbZGX6wEZB81ceyBb8AQA/APAm16TtDR3veYPr73cD+Ote25Uq+JwTPqqvLSmdhVS4dM4UvEX4TEGQS8eFbyNwgGhDxGYiAuA2FpccKKDyHFUZIRboRiMp9l96qHcHcYRl3gngu61oncnWuk8C2NX6+z8BON66GdQB/LNe25Ql+H4nfNQhXZKyA+OetD2236ILaHezXMAGKSd9T8EXOXcQglotQDlnSRb+6c1lz886vVn8Z3mhwtgILLiS5hhkZdjzMIlXLqSKchJCOi17yOokswgLjQxAbPX4eb+DZFdSEBzB4wmvbAvQr4heXBPDsUeIBRVyWdev37koASP4bmSKsu5RCJwha5yiH8fFHsTCVyX4a6NIrwlM59yU6dvmREutXlGKxeJWEiEW8JqXZQw2cpym7Dk5TdmN4LuRKcq61//gHPvqcCkWyy6ui71Xu0MClLp01lAxecoR/NOs/0Y0/aIsmSrgNS9rfiPOgAUiI/jtSBRlqdmkAvA98SSLTZwXu5fPtm0pFOT1GA6AyqQirksH8t2Oqo67r0lTGTfhmEf+RvBdyBRl3bMDeUPLOCxemd9N57anp+0Euh9ttOcqzg6W6BRK1OiYO1BlcaosG8CbOziBsjaGiWiUh4PGnH9gBN/FHXfYqepuZmbs9amnl5sjoXgJ6PCwnVDm1KRxfnOe2Mp2M7XdlFwT5z/aGO8okOe2eLySsqqcuhGj+84Ivos0FWXqG97QMuGCT9Qu3I7YOyOIzlo0bSOLGErwuvfBq1drEyze2v2WRWeuLNuuvHxr1KdZEpQhPEbwO1ASKaADlsWPYNFhEjMiTgTQzp0B3UcxTbI759vMDL84XxMs1sn9pCQJGvrHCL4HsccCa0CtRvT4YLVL9BsD6jNPo9LrJu7lxz1X9I5YkZEo55S08Eu4ijNBL0lJgob+MILfQWwJQBIJMwnaFgPeEr6VbeXEW3VB3HRekRr8qCXxESu1GtHgINHzKHMFP45ImTWSkCQoAN0DKWRgBN9F3HUtZKF7CGicBLqoe81fSA6Xm5mxN/2+vEUNHdxquicJCiKLc3ZG8F3EXddCBo57otMHe2FAoyQv3QhQboEAKeFytRrRpk12qOirI2U95lF0TxIUSNbm7PwEP4eMMbK81Nd6HdmxAxj+1CTyqytt6wcvrwCTk4r2SnO2b/deXyoB5TLAmP04OwuMjQn96Pl54B927sWd/3UcVy4vgvHe+MorQj/Xj/rVY9hbmMX5bfaxn99Wxt7CLOpXiz12HahUgGoVeOgh+7FSUb1H6sic4HMvfN56CRw8CNTr7evqdXt9ECoV4Bri3KCWknPjipPjYwewgmLbuhUUcfyDnwFOnACaTftRsNgDwL43zuGaI4+BgXzftzwS3zk4Pw985CPA0JD9fGjIfj4/H9suxEa9Djz6KDA1ZT92XnuZgmf6q15kllZQ3XVHhF8xTJRFFiewHJRmWwaYP2gC8c4jWZbdF8C9HxL6BKg+54wPP+M+fCLSoitVVL/i45Xu+vKNgQ2+ETdZPPm1IMD8wepwzHkQsnsMt3DOMedm22T9RcZFvWGovuGowAi+poTNBXAidBr5Qrvg5ws9b15Zm8DSgh4WfhMs/tBYvxuQYDyL2QUcVQuJRtPAwIsTI/gaEiUXYHrapwRwgLC6nTu7bzRpt3qUYlm+AtsAuuo7ySbOkr2RIuOiRhNp4MKNGyP4miEiFyBs0lCtZteZGRparzdjXDvy+f5P7+T+ZstbyrF//02W8z5/WE78Z/HO1SBJXlHzBTKSb+DGT/CzF6WjAdccmkQR7SGVRazgmkMBQyrn5gBOcN+FbfxIj3oduOce4CtfAZ56yj7z774beNe7gMOHsx2uJgN3NNbi40+jnt/ZFaezmi9i+LMHcPhwvBEyjJp9rQ/LF35pjr8PQSLjeFFnQaPRov5/yjCCr4DIuQCTk54hfgSGod89wP23+fl1Ya+8OIdFNoqfrOTw3YujqLzIvzAN/XPwIDAwYN9g63X7O//TiacxBgs/3lhGEwynN5XxkSE79r1SAfbti3EHy+X+1odk91991NM0IQA4wD9XHc5f5X1T4K3vQoMwbK3gmf6qlzS7dCIPM/2iPoKQoSxLUfQb7eGukLl163pd/htvtL/y8fH298XuTutxDgib04k4VxC5qqfx4bctyoWdt6Ra8C3LbrPnPgkLvSNs1uDcMIJWOjSVEvunn5BW5+bgvOe22+yv+LrrbK0ZH/epzx8T7uiXJmO0yMr0gY2W+DkdH8EPvP2oUTYmSscIvlKiJr1wrLOg4WpNToneWKs1qiLCxR80pNWpnTMzY4s7QJRrzZHefXf7tlRNlHd2fnP2+brrBO8XJ95/9YqSiQqThBF8zRBRwO3I7vXYZEe4AluKMSXd6IaXe6BpT1MGFv+guRNOdUzArpB5AnZXrUXW3lN3YkJNOKzXiMXxfIjsEXFsv0UX0D6avYBC4qrTRsa0OMyu4Dc5PvhAYWoiyKjgc3MXOL7dTr+90yt3587eVnCtRjQwQPReWHQ+513VVLWV7x6xjIzYxyYyIW962r6huUtarGwr0+OVjLVSNE3Msy34vE5L54oxCW5Gml90EaREsmvi3C3I7sboQfzcExNEnx/o7i7mLK+OxB9774UzYhkaEl9yw5TyaBFzLoARfM1YvYLv14yDNPQECEWQJigdNz1HpHbuJLp/qN2Nxiu+xmsl6V4aYMrba4Y5trCfoayUhw4TtjEbWEbwdUOxhZ2Wrl994zHZHcTqmpqyXTMX8sHCA6eniRq5vO/nqLbw26xtq7suU19RY35YdtOXBhi9OlKOV3B1Cck0Fn62BV+HsMg09PXtFycU0c/ydsTA8d+vf0/e73f/Zm6fv99nNAE6slutD9+9r2cGvEecZwYijjgV53toM5I1PvxsC/6R3RZdLLSfABcLfSSTCCJstc6ksiZyHIvr7GCJJibs99ZqRB/YaNFrnVUefUZlzg1ldZgzKe6IHnJKY/A7kVVI7fTmsud2T28uC9nvXigPjnBjonT0FXzZNbR1aECu3LeqEJ5L676CRfcPWXR6s52MdJn5u2UIaItsOrbfsiNwevyPjIqUkfDb3wjEWZHTkwwWTiPyF3xTS8eDHTvWa6AA60XHduwQs/35eeDeI2MY+vEJoNnE0I9P4N4jY7EVz3KO5/Bh4JOftB/dx5t2nhoZw/P77X6uTTCcGSnj32+cxTXXAo9d/ABKry2CESFPjZ7boldeBXI5nH/9KH7q4Y/afYV7wATXq9EVls/3tV44Bw4Axfa2ligWA9XwSS28O4HqRbVLR3sfd4QhYha7APFwu7V6uWICWe49lgaYfueSrLwMSSOHftDhOo77eoNx6fRJXJMsIUU7ckEpAxF1u7WCCHbUpQlo50I7usei8x3ZsOdRoKN7Ip5Pil0quuQBxL0f0gUfwDsBfAfA9wB8wuP1QQB/3Hr9bwCM9tqmUsGP4USNIto6RPkkHa+LMA7BX9lW1m40dccdtui7jY+jeyy6445o21Ud/qvTSDbOOTOpgg8gD+D7AN4MYAOAbwO4vuM9ewE81vr7XgB/3Gu7KgU/jtn9SKKd1UxZgXiJwdnBaC6dXkvWSlBPT7eXVRCZ0JVE4oqKky34twD4muv5AwAe6HjP1wDc0vp7AMBpAMxvuyoFP5b43SiindHoA9kc298jRt/DPRNY7Fk+U2JvaEcXC19ElM4bAbzgen6ytc7zPUR0GcAygFLnhhhjE4yxBcbYwqlTpwTsWjhGHvGe3R95RODsfpROPAcOoDHYvn+NwYxHHwjgqZEx9HNJsFIJCBBxcrFQxN5NT6B+9ViU3UsUBw8CxyfngNFRIJcDRkdxfHIOBw+q3rP40SkqToTgczuY9fkeENEsEd1ERDddddVVAnYtJGNjwOys3e6NMftxdtZeL4oIol2/egx7C3ZYIRjD+W1l7C3MZkpQZLBvH/DNmz/o0TzSg2IR+MxncPw/PIEVtP+OqyhgpVhCE/Zv89zHZ4E9Y5kKfb1reQ5vengCWFy0xziLi3jTwxO4azl7rTTdrUUB+zHuHsZr8Ez/oAtS6NKJgyjJVzpNRqWSapUuszw1YWfFnsUm232Tt9c1nISscpkWbq62FcNbHS7R/UMWvf3t3VU1M/UbGbejMiDZhz8A4AcA3oT1SdsbOt7zYbRP2h7utd20C74RbX2ZmbGnUm6/3X6sVm3RPrqnO+qkaynaUShZzWJewwQWKEOq4Nvbx50Avgs7Wmeyte6TAHa1/t4I4E9gh2X+LYA399pm2gXfoCdO5yen/Z/TuerGG4lOoOwv9q7JfSciw2lW7t6+rjd1oUaIsfCVIV3wZSxG8A0q8BK922+3r5QGpxdwd/QOo61bbbFnbP3moXsDEJEJQiYGXx1G8A2GkDiiNz5O9HxAC38pV14TG8c9ND6ut9g7iAofVB2Dr0uWrQqM4BsMIegUiUO39i6XfLHQbcWOj9svJ6IMtcqGJYJxAiOc41nZVk708QTFCL7BkywPe4Pg/n4c8bvPKuQAABp8SURBVH/4Zy16HuvFuJ69pepbnCtRZagVNywRjmXRakGDjlcxYwTf4EmWh7394HwvMzPtj9Wqv48+ad9v2mo08XpHp33i2E/wTT38DOMkgNxzD/Dgg+vZgE6CiMHGSZy5fNl+/I3fsB9PnAB+53fs9UB3Qo1WCTcB2PjSEnd90jJkj0/OofCTl71fXPI+zizA7BuCftx00020sLCgejcywYMPAg89BExN2anfhowyOmpnxnbwQq6M7z19IlGGwPKWUYyc6T4WAHbm/IkTse5PnDDGniGim7xeMxZ+xqnXgUcftcX+0Uezk/pv8ODOO+1SIi6aYMDddyZK7AFgZNnHis9wzSkj+BlGp6JOBsXMzQFPPGF7uV3kQLj26Sfs15MErwhhqSSkJtbBg93XSb0O7V1fRvAzzKc/DTzwQLuP+YEH7PWGjDE5Caxw+vGurNivJwleP9vPfEbI5mX3vZZFZgQ/qXdkmXz848Dw/r1o5gcAxtDMD2B4/158/OOq98wQOz0mMilpE52SK94mNeAhM4Kf1DuyTCp/shf3rz6KXLMBAMg1G7h/9VFU/mSv4j0zxE6PPgxnRwL0adCMgz8cQ/0PTgDNpj1JOzYm1MirVIBq1Q54qFb1F3sA2YrDT1QSTBzk895xyvm86j0zxI1l2UlJnAqgSUxWkp0HoauewCRerRNXX8kghK43YrX/T+iL0a8mjCF7OOeVc9N3kpQSKPYOskQ5Sj8L2RjBb3Fsv+WbBh83YSoKHtntnf5+ZHf/x9LIeVv4jZyx8A0CEGWYRESGkXdkt0WNgQ3t183AhlDXoWiM4JP6cq2ehKgZLjL9feHmalcj7iZACzdXwx6RwUBEzrnVXk46rGESBWlulxKnbEOpJOgDwmMEn4jOXFn2/IHOXFkW+jl9EaYrkMhOQpZFNDDQvp2BgUQP4Q0aYFldYq+iLo9UH77G7lA/wc9MlA4v8843I082vMgIv4iJMP/DY3JyvRCMw+XLyYu5NujF5CQYpxX80Kn4rrewtYzSHMKdGcEXKpSCOD52ACtoTw5ZQRHHx3xSvw8cQGOw/X8ag8Vw6eK82OqkxVwbtIIWfc6fGK+3ffu6QyUrFXu9H4FCuEsl73/mrdeE7Ag+L/NOYV2Np0bG8Pz+9uSQ5/fP4qkRfnJI/eox7C3M4vw2+3/Obytjb2EW9atDJJRoeBM0JJ8L27zPHwJLRB2bIElVT77jM2jmC23/18wX8OQ7xGTySoPn61G9SAnL1CRqIAoim5aIjPgxJBuhzXAsiy52NB5pgtHjg1UtwhYD0aPzlwnLTILgG9rQ+aQ1xIvoCc4juy06taldMBPTTS1g5y+TeGUEP3HoetIa4kfkuZDk86qf0GedEjkdjOAbfNHxpDWoQcS5kLTWjp3wQkqbaA991vWm5if42Zm0DcPcnN0FKJezH5NWEzwApgGKwUHUuZC01o6dsLL3pLN7fWJ7SfDuBKoX5ZO2XsWkElpEikfSLTGDOBJxLsQVdBHg2hc6ye3aZqjaWh3AuHSofwEPUfYgacg4aQ3JRPtzIeD1K+w4JNxceu2bqPIvRvCJ+hdwkSUMDAZDJIKWRtF5pNJz3wQZmX6Cnx0ffr9ZpQGSktKcgm0whEHWNTHMKYHSuV7nTlQ99y2GzPfsCH6fWaVP3uxdwuDJm9czBU0XLYOhHVnXBONcpxeu2t51M6m8OIfnLo3itx/K4blLo6i8qE+whe++xZH5zjP9VS+qffhBk5Kc9zlZeSvbyqma2DUY+kVK3wlOMlTXNRkwaUoJPfbN+PAFEmYGPFCcrWXRaiHd0TwGQ2AkRrcd22/RKVaiJuy+DadQ6hJDkf0iRNNr30yUjkDCTub0SkRZHeY0QkhRNI/BEITpab6oRb0enJF0L+s9aNKUCjqbDa3vG4R+jp/gZ8aHH2Yyp1ciyvHJORTOvuz5v74lYg2GFLJjBzD40qLnaxRx4nF+Hvi94iTyqytt6/OrK239G4IkTQVBxuQzy+f7Wi8F3p0gyALgdQD+AsBzrcctnPc1AHyrtRwJsm3VTcyDjAh4oWK6DCENhljx6XQlorNckxMq3XSHSgtyKUkJ7+RoBcVo4UcV/IMAPtH6+xMApjnve63fbcsQ/H5qXwRK4OCdgECifPhHdq9PTjtJJlol3RiSAS+OnDEh10PgNqWCkqaE18qJKZlTpuB/B8AbWn+/AcB3OO9TLvhS7ti8H1CDRsaBCRr9YDD0gpesKMqCVVDuRGhhwZj2X6bgn+l4/irnfZcBLAD4awDvCrJtGVE6wlPHPX7AMGFUSuHctIxLytAvsUTIxNjESEo1zBj2P5LgA3gawDGP5Zf7EPyrW49vBnACwE9z3jfRujEsbN++XfgXIYO1mGNXGJUuqdyBMCUkDILQpoOaAFGV0RwornpFyl06Hf/zhwB+pdf7klIPX/uiU73gWPiXNm5SvWeGJKK6jaggt4mMm1dcdX5kCv6nOyZtD3q8ZwuAwdbfW1sRPdf32nYYwU+8+KrAsqjB8l2C3wRoaVdV9d4ZDP0hamJU0gRrHE1T/AQ/ahz+pwDczhh7DsDtredgjN3EGPtC6z1vAbDAGPs2gDqATxHR30f8XE927AC+tGsO518/CuRyOP/6UXxp15ypbePH2Jh9KnfAAFx9ZDb+/TEYQnLwoE+8f795AJIKmVUqQLUKPPSQ/Rh3UbeBKP9MRC8D2OmxfgHAr7X+/isAPxflc4JSeXEOv3BpAvmX7OSMoZcWcWhwAvkXAWAsjl1IJAxNz/U5NGLeE4MhPDt2ACfZdlxLHslf/RYg274dWBSwnQ46kzkrlXhFP12ZtpO9M/EM7Rw8CFBOgwxAgyEilQrw3D+9E02wtvWdVW6D8OTNB9Bk7ed/k+X73o4bHdoipkvwY6gnrYKDB+0yDu7+uscn54TU3d+xA/j9wgQ6nTp2zNRE9A8wGOJibg6/+IMnkHOdzQSGP8D7sfmD/Y3w33r+L8GofYTLqIG3nv/Ltc/qt9+1Fr1+ec591UuYSVudK+VFQVTZVB61GtHnB6p0CXlqAnQJeTNha0geInNK8t2BDAQQ5fP6hJ9yQFaKpz1d8W5a8nQl/DAsLvys+BvmJlFEu6uqiBXcMCfOVfXr7BDehyewPFJGnjWBo3+Op8bEjCIMhjjgTdhuPBVihN/gzF81GnhH3dt1/I56AlzHvDuB6iV0HL7qOOCQ+FrxkpOjJiaI7itY9FrH57+WtKxhQ6bh1do5vbnc/8Z4JSKc607jZEVkxcKXQVx9a32teImtz+p14MtfBg5tmcSmjs/fxBlFrH0nLj/m+deP4sl79WklZ8geI494j/D340DfE6Pdgcqu9XG0IpQF706geglj4cvKjhOdYu2Jj9Ug04e/lqzWh9VSqxHdt8Giix2dvi4W9PFjGqKhdRKjzyheVOXXkwNlz+vh5EA5UhtF3vd6xx1iul0R+Vv4yoWdt2gzaWtZ1BjY0La9xsAG8a4in8w+Ua3Pwn6+F8tbvN+f9Alyg02tZlckmJlZf751q/1cqejHVHHy6B5vF+fRPVYkI5BXXuHoHnFGXWYEX4Zv7VzRu4XhuaLYEsiPVyy6gELbZ1xAgR6vxGMx9z2K8PNvGlLBzIz9c46Pr4u96sKAgWviC+DoHoueR5kaYPQ8ynR0j30tRB39eDZ5F1jKITuCL6H+RVx9KG3Bbx9JXMCG2AS/r1GET2cj08s3XYyP2z/rbbepF3uigF2vBHLbbevHLwTeCEWgAZUdwY/gW+MRl+DH1Q1HBDzXWRNiOhsZ9MCxRB0L99CtGvy2MV4nzgjnttvsR8e9FQnO/vN0xlj4PsiYYD03xHHpDAnuauXjjorFh98HPOu+CSi3AA1i8HLxOT5spcTkw3fE3hH5zudh4Y1QvJYGmPHh+yGrq1Uj3+5bb+QLsU7ays60FbWvK9vKekRxGCLD85WfQkn5Td3TBy6YO+7oFveZGXt9FHjfK8+AMlE6YYiQjBVXWKavqOvm7lHQW9QQMzxfOUBHdqtrcu9EDx3dY18XTWaL/tE96ka8feF17fCs/pDXd6YFP2psflzxyL5uG40y+9a+D9dNdGVb2cTfp42StyvTGcmpmsCdnvYOYUxUVninAVqtCp17zLTgp6KgmkYWflxt2gyK8RH8Bpja31uj60EEor0IfoKf+tIKQ5zCSbz1OnJ87ABW0J4yvoIijo/FXxTOKel6zz3Agw+u1/eOu3OPQTKvvMJ9iVgOlRcVltFIWRn0+Xng3iNjGPrxCaDZxNCPT+DeI2NSyianTvC7at8kue5Fi6dGxvD8/lmgXAYYA8plPL9/Fk+NyOni1at+UOXFOTx3aRS//VAOz10aVXvxG+Tgc33kqYHG/ROBasBLIc5rOkTd+37Zt6/bYKpU7PXC4Zn+qpewLp3O4dHqcKkrgzVqbD4RJbYqZxB8h5gSch0MGuI1uejjFp2eJruHglNHPm/3VJAxkRpb1JpPcII2dYU8QKZ8+B6CdAEbaPWKkrAoG90bIETGR9RTMSdiCIZl8RuBoJVo12JpV7UreagJSGmkE1teik/4ceR5K4kGY7YEP8CETtS7c+pFz+c75CddmRo6aaJnFdWOa6rBvG8MDZZXdgyR4Rx7A4wmJiJsV3JYs5/gp86HH2RCp1//WGc3qqGXPLrZI1kTwb74fIes9DrPl3jrDclkxw57Qv78VRy/OGPAgfWggc7+r73WJwLOnMBJth333ht+s8u/PgmstPeewMqKvV4yqRN83gnKPXEDcNfyHK57+N8Bi4v2/ZhHgiaC/ZDxHRqShRON9bGVA7hYKHa/odi+juXzntvhrU8EBw50HWcTDP8zfyeA8I2Qhpe9DSreepGkTvBl9LW94fMfxSAu+b6nMVhss3iSjO93yAvX8wnjMySTSgX4/r8Yw32XZrE8UGrvAnXuHBr3T6x1OXvhromuLlHUWp9YxsaA978fBLa2KgfC/fknYN05h3e/2x4J9Qt7HWeUzFkvFJ6vR/USKfFK9IQId9IKcrtgqYT3HaYs6cXAp1YjGh623cuLrOw7bzU9TfTsLVW6hDw1AbqEPD17i5wonbiYnubP1y2ycmg/vuyCjMjUpK0EfEsktwT/4FutyIWVdMOrrMTjFYsuDKQ4QslARO0Z1LUaUYPX/6BV3iONGdh+xx0lSIFb098xnCIaqH6CnzqXjgzOF0ue6xkAEGHopUV8+FsT+PTPpysByZm4c5Kw6nXgN58Zw4cLszi/rQwwhvPbythbmMXmD8pJAjOoYX5+PYO6UgHOjvgnO7nfD6zPAcjIFo2LSgV4dbP3cb/AtvfdGN3hAmcujAH2POGExKQ23p1A9RLVwhdZ9OzIbosu5du7Ucl2a2jRRLoVd98Ao1dH1t1WjvU2NZV8K87QGycR70K+I79loGjH2WvSp0EKlkWrhe4QymP7rdDnvlceT+cSpWUjsujSEV7W2LLo1RFb/LjdaQRWr1Q+RPaIFV4trMcKT03Zq6emYtofgxLczcsnNlu0vMW+Bpa3lOnzA1W9+jRISGZydORcfjM14epMtXlzpJvbek1/by2J0rIxk4IvugSAc+IffpfF92cKnriMo9EDD16jhtOby8bCzxDOSNM94nSe8yY0VUzgy8h+d87zpV1V7+McGAilJ23GG68qaYTvMJuCLzCaxPmBju23qJHjZBSGbEfGRXGTEd7EUgOgTZtoLUIhDZNzhpBo1KdBRvb72k3Op7xEmC5vbT0lNni4igvROuplU/AFnoxrtTt8ikmFbUfGhXfDKgnupdvn5zcBel++3TWmcyEpgzi65pV0CtGVefPhuXARrTcAbxR9djDaNe4n+KmN0hGZLbpvH3DDnEc6tAtWKgktZ0qc8gb08svxlKXlJJExAH/YfB8qO9fLxUor5WrQih07gC/tmsP5148CuRxWTr2GVWxoe4+qPg1SSybn+DJ5ofi60JFIvMzaTauvhI4A6kVqBV94xm3MzRV4YXAMACbl19zA2FhX5uTaPjhTTYuLbdmWhnRTeXEOhy5N2LWkiFBceRn5HAGlUix9Gnw54H29C8l+HxrivrRh5WXctRzu/Gecm9Hqtu3ywll5pn+QBcB7ABwH0ARwk8/73gngOwC+B+ATQbYtJPFK4Kx9z27zov2WluWT8CXfR1qr8RPORPpJDQlCJxdOB8Kj8tz4VQwFiDZtCrddSfN0kOjSOQbg3wL437w3MMbyAD4H4A4A1wN4L2Ps+oifG4yxMeDECaDZtB/HwlseJ/d2txlsQ3ThtLExXBr2Tvi6sE1+EbP5eeDSFd6f30lqqoQa/NG4taDUNoE9rm06dy7cdsfGcPxjs3ghVwaB4YVcGcc/NhtJp3rCuxP0swD4BjgWPoBbAHzN9fwBAA/02qZOpRUcju236DQrdVu+IqNn3KOSUokaA+2z+HF2lzqy26JGECtfAwvPIJ/U94Hg0aP7VxMItVlZuTZQPGn7RgAvuJ6fbK3rgjE2wRhbYIwtnDp1Kvon790LDAzY/sWBAft5BG44MIbP/MfTGIOFMyPlNb8lZsXclZ+8d87uFeqUYX75ZYAIywMlNMFwZqSM/BclWwAuNn9wzFUn0Js0VQk1+COjEm0SOPhD2xLnzWmBhZNRJeUoeHcCZwHwNGzXTefyy673fAN8C/89AL7gej4O4LO9PjeyhV/lJEtUw7dck51w5FeZT1WSk58fvwlGj+WrJgY/S7RGoE0wu21oqZTesgotnOv+62/xbuO4cLP4No5RgOw4/B6Cr8alw0uWyIdrueb86BMT6xUE3dUEhZzovCp6nIqEsdDDnbO8pf/EE0Pyia2RuCY4197/uXG9BDTl85EMSFn4CX4cLp15AP+EMfYmxtgGAPcCOCL7Q6nh3VqNt74XzvDr3nvtCpKA/fxLX7Kfh2mE0AVncsgJ31JRgbCZ8+9YNHxmycTgZ5Ab5iZRRHteShErdr5KynC6WlWrwC3PHMInpy7jGzXCwYcvA4cOqd25fuHdCYIsAN4N2ye/CuDHaFnyAK4G8Oeu990J4LsAvg9gMsi2o1r43BIIuehNlaW5dgTX/4lKrUb0WK57GGsmbA06lVWQTa1GNDJiN4OZmrIfR0b0LScCWRY+EX2FiK4hokEiej0R/ZvW+heJ6E7X+/6ciH6GiH6aiGKZ4fnm271brn3z7dFbrlUq9t3+oYfsR2fSJSr1q8ewtzCLi61wTAJwZnUIx/9ezPb7ZX4e+JmnD4FVqwBjXd+nmbDNMDIzWzWECLh40Y7uZsx+DoTva6uK1Gbann34EL44WEWD5UEAGiyPLw5Wcfbh6EOweh149FFgasp+FJUGPT8PfOQjwIbL5wHYWbUlvIyf+bTEhgg+7Ntn71P9PYdQ/3oTH9ps4fy2MogxvLzZbnxSv9o0Pskcc3O4+MprXQaAsrIKkpmfB/7sz4D3vAf4oz8Cdu2ynwt158YFz/RXvYiIw5+ZsUeYt91mP87MRN6k/Dr1mmUzxjJZbUgOvJj0Uim1UTpE6+f9+LitJePj+laJRRarZbp/IEDcDyS7E1VTQg/NqJj694Y1NDNI4qDTqHNrio74CX5qXTrz88ADDwBf/artevnqV+3nUSNc9u3r9tmLrBbJK5sQRzkFHrLmLAwJROPyCrJwJ0jV67aWjI8DX/6yOHdubPDuBKoXURa+shaBYdEsUofIWPiGdXhFBKP0YE0KSdEUZNXCjz1tWQRjY8h/cRZnRspKyil0Uq/bE1OHDwOf/KT9eM89CbRsDELwKiK4giJO7k3fZG0nidUUF8y+IejHTTfdRAsLC6p3QwmOyFardhSQ+ySLm4MH7SgE9+fX6/ZJbhKussnxyTkMf2oS1zSXcDK3HWc/cQA3HDDRWrrAGHuGiG7yfM0Ivl64LWrHZ+h+bjDowIMP2nM6U1P2yM+gD36Cn1qXTlJJw7DRkG5k5aEY5GMsfIPBEBgzAtUfY+EbDAYhmBFosjEWvsFgMKQIY+EbDAaDwQi+wWAwZAUj+AaDwZARjOAbDAZDRjCCbzAYDBlB2ygdxtgpAIuq96NPtgI4rXonYsYcc3bI4nEn8ZjLRHSV1wvaCn4SYYwt8MKh0oo55uyQxeNO2zEbl47BYDBkBCP4BoPBkBGM4ItlVvUOKMAcc3bI4nGn6piND99gMBgygrHwDQaDISMYwTcYDIaMYARfEoyx32KMEWNsq+p9kQ1j7NOMsf/HGPs7xthXGGNXqt4nWTDG3skY+w5j7HuMsU+o3h/ZMMauZYzVGWP/wBg7zhj7qOp9igvGWJ4x9k3G2FHV+yIKI/gSYIxdC+B2AEuq9yUm/gLAzxLRPwfwXQAPKN4fKTDG8gA+B+AOANcDeC9j7Hq1eyWdywB+k4jeAuBmAB/OwDE7fBTAP6jeCZEYwZfDfwawD0AmZsSJ6H8R0eXW078GcI3K/ZHI2wF8j4h+QEQXAXwJwC8r3iepENE/EtGzrb9/AlsA36h2r+TDGLsGwF0AvqB6X0RiBF8wjLFdAH5IRN9WvS+K+ACAr6reCUm8EcALrucnkQHxc2CMjQL4eQB/o3ZPYuH3YBttTdU7IpIB1TuQRBhjTwP4KY+XJgHsB/Cv490j+fgdMxH9j9Z7JmG7AObi3LcYYR7rMjGKY4xtBvDfAXyMiM6q3h+ZMMbuBvASET3DGPtXqvdHJEbwQ0BE7/Bazxj7OQBvAvBtxhhguzaeZYy9nYh+FOMuCod3zA6MsfcDuBvATkpvcsdJANe6nl8D4EVF+xIbjLECbLGfI6Ivq96fGLgVwC7G2J0ANgIYZoxZRPSrivcrMibxSiKMsRMAbiKipFXb6wvG2DsB/C6AXySiU6r3RxaMsQHYk9I7AfwQwDyAPUR0XOmOSYTZlssTAF4hoo+p3p+4aVn4v0VEd6veFxEYH75BBI8AuALAXzDGvsUYe0z1DsmgNTH96wC+Bnvy8nCaxb7FrQDGAfxS67f9VsvyNSQQY+EbDAZDRjAWvsFgMGQEI/gGg8GQEYzgGwwGQ0Ywgm8wGAwZwQi+wWAwZAQj+AaDwZARjOAbDAZDRvj/8a+JhbFDwrIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_predictions(x_test, y_pred, y_test)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
